From http://www.chabad.org/library/article_cdo/aid/623729/jewish/How-do-I-kosher-an-oven.htm: "If your oven is of the self-cleaning variety, koshering it is fairly simple. All you need to do is self-clean it". Is this — that no other cleaning needs to be done and the oven is kashered — true even if food residue remains after the cycle is completed?
The food residue is burned to an ash and therefore is no longer food residue. It is better to clean out the ash, but that is more of a practical matter.
Utensils used directly in the fire, (e.g. BBQ grate) must be kashered by placing them into fire. This process has the effect of burning any absorbed taste. To qualify as a complete libun, metal must be heated until it glows. A self-clean cycle of an oven (approx. 850° F) also qualifies as libun. There is no need to wait 24 hours before libun, though it is advised. There is no need to scrub the utensil before performing libun, since the fire will burn off residue, but some cleaning is advised.